Photographer René Burri's best shot

In 1958, a year before the revolution, Magnum wanted to send me to Cuba because they had contacts with the rebels. I'd just spent six months in South America and said no, so I missed everything.

Fortunately, a few years later, I got another phone call. Laura Bergquist, a star reporter with Look magazine, had met Che Guevara at the UN in October 1962, after the Cuban missile crisis. She bugged him so much that he told her: "If you get permission from the CIA or the Pentagon, you are invited to Cuba, and I will show you what is really going on." She got the green light from the Americans – and I went with her.

We arrived at Che's office on the eighth floor of the Hotel Riviera in Havana. At that time he was the number-two man in Cuba – he was the minister for industry, and director of the Banco Nacional. His face was on the two peso note. I saw the blinds were drawn and, after we were introduced, I asked him in French: "Che, can I open the blinds? I need some light." But he said no. I thought, well, it's your face, not mine.

Immediately, Bergquist and Che started a furious ideological dogfight. She had to take back a story for the Americans, who were still angry about the revolution, and he was trying to convince her that what happened had to happen. For two and a half hours I could just dance around them with my camera. It was an incredible opportunity to shoot Che in all kinds of situations: smiling, furious, from the back, from the front. I used up eight rolls of film. He didn't look at me once, he was so engaged with trying to convince her with maps and graphs. She was a chain-smoker, and he occasionally lit up one of his cigars.

We went back to New York, and Look ran a 16- or 20-page story. This picture was only an eighth of a page. It certainly wasn't a photo essay, like the one Henri Cartier-Bresson did for Life magazine at the same time. He was in town with us, but only got to shoot Che at a press conference.

After Che died in 1967, this picture took on a great deal of iconic significance. Even before then, some kids from Zurich approached me wanting to make a poster from it. I never heard whether Che liked it or not; there was no response from Cuba at all. A photograph is a moment – when you press the button, it will never come back. This picture is famous thanks to the chap with the cigar, not to me.

CV

Born: Zurich, 1933.

Influences: Cartier-Bresson ("my teacher and friend"), Magnum co-founder David Seymour ("he threw me into assigments like a baby into a swimming pool").

High point: Meeting Picasso. "The man was tremendous."

Low point: Being mistaken for a spy. "Every time I walked away after having a gun held to my head, I thought: you've been lucky one more time."

Top tip: "Be curious, pushy and diplomatic. Everyone takes pictures, so you need to have your own opinion."

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